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Question: Planets orbit the sun in the path which are:...

Planets orbit the sun in the path which are:

Explanation

Solution

A Planet is a non-luminous heavenly body that means these objects do not have a light of them. A star is a luminous heavenly body which means they have their own light. Planets always revolve also rotate around a star, the collective family of stars (in our particular case sun) and other heavenly bodies revolving (the planets, the satellites’ of planets, the asteroids, etc) is said to be the solar system.

Formula Used:
The general equation of ellipse x2a2+y2b2=1∀a>b\dfrac{{{x^2}}}{{{a^2}}} + \dfrac{{{y^2}}}{{{b^2}}} = 1\forall a > b

Complete step by step solution:
The planets revolve around the sun in an elliptical path known as orbit.
An orbit is the well defined path on which a planet revolves and is found to be elliptical.
Johannes Kepler with Tycho Brahe studied the motion of planets around the star and concluded that the orbits of the planets are not circular but elliptical.
Kepler gave three laws in order to explain the solar system which is as follows:
First Law (law of orbits): Each planet moves around the sun in an elliptical orbit with the sun at one of the foci of the ellipse. Obeying the equation x2a2+y2b2=1∀a>b\dfrac{{{x^2}}}{{{a^2}}} + \dfrac{{{y^2}}}{{{b^2}}} = 1\forall a > b
Second Law (law of areas): The line joining the sun and a planet sweeps out equal areas in equal intervals of time. In simple terms the areal velocity of the planet around the sun is always constant. Mathematically, dAdt(areal velocity)=Constan⁡t\dfrac{{dA}}{{dt}}(areal\,velocity) = Cons\tan t
Third law (law of periods): The square of the time period of a planet about the sun in an elliptical orbit is directly proportional to the cube of the semi-major axis of the elliptical order. Mathematically, T2αa3{T^2}\alpha {a^3}

Note:
All heavenly bodies revolve around a star. The revolving orbit is not exactly circular but near circular also called elliptical orbits. Like IUPAC there is an international organization which governs the disputes and matters related to the solar system named IAU, International Astronomical Union formed in 19191919.